{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "XXDeo-aGOAXF"
   },
   "source": [
    "##### Copyright 2020 The TensorFlow Authors.\n",
    "\n",
    "Licensed under the Apache License, Version 2.0 (the \"License\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "9XRGdjHNOE9D"
   },
   "outputs": [],
   "source": [
    "#@title ##### Licensed under the Apache License, Version 2.0 (the \"License\"); { display-mode: \"form\" }\n",
    "# you may not use this file except in compliance with the License.\n",
    "# You may obtain a copy of the License at\n",
    "#\n",
    "# https://www.apache.org/licenses/LICENSE-2.0\n",
    "#\n",
    "# Unless required by applicable law or agreed to in writing, software\n",
    "# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
    "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
    "# See the License for the specific language governing permissions and\n",
    "# limitations under the License."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "KJihamFwOLUT"
   },
   "source": [
    "# Variational Autoencoder\n",
    "\n",
    "<table class=\"tfo-notebook-buttons\" align=\"left\">\n",
    "  <td>\n",
    "    <a target=\"_blank\" href=\"https://colab.research.google.com/github/tensorflow/probability/blob/master/tensorflow_probability/python/experimental/nn/examples/vae_mnist_advi.ipynb\"><img src=\"https://www.tensorflow.org/images/colab_logo_32px.png\" />Run in Google Colab</a>\n",
    "  </td>\n",
    "  <td>\n",
    "    <a target=\"_blank\" href=\"https://github.com/tensorflow/probability/blob/master/tensorflow_probability/python/experimental/nn/examples/vae_mnist_advi.ipynb\"><img src=\"https://www.tensorflow.org/images/GitHub-Mark-32px.png\" />View source on GitHub</a>\n",
    "  </td>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "B0HrNKbJw2bA"
   },
   "source": [
    "### 1  Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "cellView": "both",
    "colab": {},
    "colab_type": "code",
    "id": "cttwhYKYGhPj"
   },
   "outputs": [],
   "source": [
    "from __future__ import absolute_import\n",
    "from __future__ import division\n",
    "from __future__ import print_function\n",
    "\n",
    "import functools\n",
    "import sys\n",
    "import time\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import tensorflow.compat.v2 as tf\n",
    "tf.enable_v2_behavior()\n",
    "\n",
    "import tensorflow_datasets as tfds\n",
    "import tensorflow_probability as tfp\n",
    "\n",
    "# Globally Enable XLA.\n",
    "# tf.config.optimizer.set_jit(True)\n",
    "\n",
    "try:\n",
    "  physical_devices = tf.config.list_physical_devices('GPU')\n",
    "  tf.config.experimental.set_memory_growth(physical_devices[0], True)\n",
    "except:\n",
    "  # Invalid device or cannot modify virtual devices once initialized.\n",
    "  pass\n",
    "\n",
    "tfb = tfp.bijectors\n",
    "tfd = tfp.distributions\n",
    "tfn = tfp.experimental.nn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "nbQ3rcTowypZ"
   },
   "source": [
    "### 2  Load Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "cellView": "both",
    "colab": {},
    "colab_type": "code",
    "id": "rjgnFMxvG9Ab",
    "outputId": "7663315d-4c97-4292-e716-b84c6720cc6c"
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAsgAAABmCAYAAADWImfBAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nIAMAQPAf54Ol6s9NS0AAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1000x200 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "[train_dataset, eval_dataset], datasets_info = tfds.load(\n",
    "    name='binarized_mnist',\n",
    "    split=['train', 'test'],\n",
    "    with_info=True,\n",
    "    shuffle_files=True)\n",
    "\n",
    "def _preprocess(sample):\n",
    "  return tf.cast(sample['image'], tf.float32)\n",
    "\n",
    "train_size = datasets_info.splits['train'].num_examples\n",
    "batch_size = 32\n",
    "\n",
    "train_dataset = tfn.util.tune_dataset(\n",
    "    train_dataset,\n",
    "    batch_size=batch_size,\n",
    "    shuffle_size=int(train_size  / 7),\n",
    "    preprocess_fn=_preprocess)\n",
    "\n",
    "eval_dataset = tfn.util.tune_dataset(\n",
    "    eval_dataset,\n",
    "    repeat_count=1,\n",
    "    preprocess_fn=_preprocess)\n",
    "\n",
    "x = next(iter(eval_dataset.batch(10)))\n",
    "tfn.util.display_imgs(x);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "sbaPm7ABwvde"
   },
   "source": [
    "### 3  Define Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "iK6_hK6RyunW"
   },
   "outputs": [],
   "source": [
    "input_shape = datasets_info.features['image'].shape\n",
    "encoded_size = 16\n",
    "base_depth = 32"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "N3Q78OptyyOx"
   },
   "outputs": [],
   "source": [
    "prior = tfd.Sample(tfd.Normal(loc=0, scale=1), sample_shape=encoded_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "height": 268
    },
    "colab_type": "code",
    "id": "96g5flbdy6lK",
    "outputId": "f6a81f58-1247-4897-d19a-238708776b84"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== encoder ==================================================\n",
      "  SIZE SHAPE                TRAIN NAME                                    \n",
      "    32 [32]                 True  bias:0                                  \n",
      "   800 [5, 5, 1, 32]        True  kernel:0                                \n",
      "    32 [32]                 True  bias:0                                  \n",
      " 25600 [5, 5, 32, 32]       True  kernel:0                                \n",
      "    64 [64]                 True  bias:0                                  \n",
      " 51200 [5, 5, 32, 64]       True  kernel:0                                \n",
      "    64 [64]                 True  bias:0                                  \n",
      "102400 [5, 5, 64, 64]       True  kernel:0                                \n",
      "    64 [64]                 True  bias:0                                  \n",
      "200704 [7, 7, 64, 64]       True  kernel:0                                \n",
      "   152 [152]                True  bias:0                                  \n",
      "  9728 [64, 152]            True  kernel:0                                \n",
      "trainable size: 390840  /  1.491 MiB  /  {float32: 390840}\n"
     ]
    }
   ],
   "source": [
    "Conv = functools.partial(\n",
    "    tfn.Convolution,\n",
    "    init_kernel_fn=tf.initializers.he_uniform())  # Better for leaky_relu.\n",
    "\n",
    "encoder = tfn.Sequential([\n",
    "    lambda x: 2. * tf.cast(x, tf.float32) - 1.,  # Center.\n",
    "    Conv(1, 1 * base_depth, 5, strides=1, padding='same'),\n",
    "    tf.nn.leaky_relu,\n",
    "    Conv(1 * base_depth, 1 * base_depth, 5, strides=2, padding='same'),\n",
    "    tf.nn.leaky_relu,\n",
    "    Conv(1 * base_depth, 2 * base_depth, 5, strides=1, padding='same'),\n",
    "    tf.nn.leaky_relu,\n",
    "    Conv(2 * base_depth, 2 * base_depth, 5, strides=2, padding='same'),\n",
    "    tf.nn.leaky_relu,\n",
    "    Conv(2 * base_depth, 4 * encoded_size, 7, strides=1, padding='valid'),\n",
    "    tf.nn.leaky_relu,\n",
    "    tfn.util.flatten_rightmost(ndims=3),\n",
    "    tfn.Affine(64, encoded_size + encoded_size * (encoded_size + 1) // 2),\n",
    "    lambda x: tfd.MultivariateNormalTriL(\n",
    "        loc=x[..., :encoded_size],\n",
    "        scale_tril=tfb.FillScaleTriL()(x[..., encoded_size:]))\n",
    "], name='encoder')\n",
    "\n",
    "print(encoder.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "height": 302
    },
    "colab_type": "code",
    "id": "P6cn2Qhh0lkz",
    "outputId": "389233d0-c0bf-4498-c620-099da36831d7"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== decoder ==================================================\n",
      "  SIZE SHAPE                TRAIN NAME                                    \n",
      "    64 [64]                 True  bias:0                                  \n",
      " 50176 [7, 7, 64, 16]       True  kernel:0                                \n",
      "    64 [64]                 True  bias:0                                  \n",
      "102400 [5, 5, 64, 64]       True  kernel:0                                \n",
      "    64 [64]                 True  bias:0                                  \n",
      "102400 [5, 5, 64, 64]       True  kernel:0                                \n",
      "    32 [32]                 True  bias:0                                  \n",
      " 51200 [5, 5, 32, 64]       True  kernel:0                                \n",
      "    32 [32]                 True  bias:0                                  \n",
      " 25600 [5, 5, 32, 32]       True  kernel:0                                \n",
      "    32 [32]                 True  bias:0                                  \n",
      " 25600 [5, 5, 32, 32]       True  kernel:0                                \n",
      "     1 [1]                  True  bias:0                                  \n",
      "   800 [5, 5, 32, 1]        True  kernel:0                                \n",
      "trainable size: 358465  /  1.367 MiB  /  {float32: 358465}\n"
     ]
    }
   ],
   "source": [
    "DeConv = functools.partial(\n",
    "    tfn.ConvolutionTranspose,\n",
    "    init_kernel_fn=tf.initializers.he_uniform())  # Better for leaky_relu.\n",
    "    \n",
    "decoder = tfn.Sequential([\n",
    "    lambda x: x[..., tf.newaxis, tf.newaxis, :],\n",
    "    DeConv(encoded_size, 2 * base_depth, 7, strides=1, padding='valid'),\n",
    "    tf.nn.leaky_relu,\n",
    "    DeConv(2 * base_depth, 2 * base_depth, 5, strides=1, padding='same'),\n",
    "    tf.nn.leaky_relu,\n",
    "    DeConv(2 * base_depth, 2 * base_depth, 5, strides=2, padding='same'),\n",
    "    tf.nn.leaky_relu,\n",
    "    DeConv(2 * base_depth, base_depth, 5, strides=1, padding='same'),\n",
    "    tf.nn.leaky_relu,\n",
    "    DeConv(1 * base_depth, 1 * base_depth, 5, strides=2, padding='same'),\n",
    "    tf.nn.leaky_relu,\n",
    "    DeConv(1 * base_depth, 1 * base_depth, 5, strides=1, padding='same'),\n",
    "    tf.nn.leaky_relu,\n",
    "    Conv(1 * base_depth, 1, 5, strides=1, padding='same'),\n",
    "    tfn.util.flatten_rightmost(ndims=3),\n",
    "    tfb.Reshape(input_shape),\n",
    "    lambda x: tfd.Independent(tfd.Bernoulli(logits=x),\n",
    "                              reinterpreted_batch_ndims=len(input_shape)),\n",
    "], name='decoder')\n",
    "\n",
    "print(decoder.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "J9XuHd6Iw7_a"
   },
   "source": [
    "### 4  Loss / Eval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "z90ohRKUs0xL"
   },
   "outputs": [],
   "source": [
    "def compute_loss(x, beta=1.):\n",
    "  q = encoder(x)\n",
    "  z = q.sample()\n",
    "  p = decoder(z)\n",
    "  kl = tf.reduce_mean(q.log_prob(z) - prior.log_prob(z), axis=-1)\n",
    "  # Note: we could use exact KL divergence, eg:\n",
    "  #   kl = tf.reduce_mean(tfd.kl_divergence(q, prior))\n",
    "  # however we generally find that using the Monte Carlo approximation has\n",
    "  # lower variance.\n",
    "  nll = -tf.reduce_mean(p.log_prob(x), axis=-1)\n",
    "  loss = nll + beta * kl\n",
    "  return loss, (nll, kl), (q, z, p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "6PO6SxWm_5RA"
   },
   "outputs": [],
   "source": [
    "train_iter = iter(train_dataset)\n",
    "\n",
    "def loss():\n",
    "  x = next(train_iter)\n",
    "  loss, (nll, kl), _ = compute_loss(x)\n",
    "  return loss, (nll, kl)\n",
    "\n",
    "opt = tf.optimizers.Adam(learning_rate=1e-3)\n",
    "\n",
    "fit = tfn.util.make_fit_op(\n",
    "    loss,\n",
    "    opt,\n",
    "    decoder.trainable_variables + encoder.trainable_variables,\n",
    "    grad_summary_fn=lambda gs: tf.nest.map_structure(tf.norm, gs))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "cellView": "code",
    "colab": {},
    "colab_type": "code",
    "id": "iUmS-7IATIcI"
   },
   "outputs": [],
   "source": [
    "eval_iter = iter(eval_dataset.batch(5000).repeat())\n",
    "\n",
    "@tfn.util.tfcompile\n",
    "def eval():\n",
    "  x = next(eval_iter)\n",
    "  loss, (nll, kl), _ = compute_loss(x)\n",
    "  return loss, (nll, kl)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "QuCSidxVABmA"
   },
   "source": [
    "### 5  Train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "xKbiQZcu-z5l"
   },
   "outputs": [],
   "source": [
    "DEBUG_MODE = False\n",
    "tf.config.experimental_run_functions_eagerly(DEBUG_MODE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "cellView": "code",
    "colab": {
     "height": 1000
    },
    "colab_type": "code",
    "id": "ba5W_N6oTNbo",
    "outputId": "426e00d9-c330-4b53-e85e-b07b79b485e8"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "it:    1   ms/it:8167.5928   trn_loss:571.6944   tst_loss:542.9343   tst_nll:532.3325   tst_kl:10.6018   sum_norm_grad:2056.6118\n",
      "it:  251   ms/it:7.7388   trn_loss:188.3120   tst_loss:174.4140   tst_nll:166.6604   tst_kl:7.7536   sum_norm_grad:561.9462\n",
      "it:  501   ms/it:7.7590   trn_loss:148.8059   tst_loss:148.2165   tst_nll:137.6826   tst_kl:10.5339   sum_norm_grad:796.4335\n",
      "it:  751   ms/it:7.7292   trn_loss:141.5680   tst_loss:142.2636   tst_nll:131.5428   tst_kl:10.7208   sum_norm_grad:490.8536\n",
      "it: 1001   ms/it:7.7422   trn_loss:130.4454   tst_loss:135.6136   tst_nll:125.0441   tst_kl:10.5695   sum_norm_grad:442.8789\n",
      "it: 1251   ms/it:7.7527   trn_loss:137.6278   tst_loss:132.9517   tst_nll:121.3120   tst_kl:11.6397   sum_norm_grad:442.4716\n",
      "it: 1501   ms/it:7.7564   trn_loss:130.9861   tst_loss:130.4965   tst_nll:119.9839   tst_kl:10.5125   sum_norm_grad:524.5187\n",
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      "it:29501   ms/it:8.2219   trn_loss:103.1982   tst_loss:95.8101   tst_nll:75.4957   tst_kl:20.3145   sum_norm_grad:737.2990\n",
      "it:29751   ms/it:8.2706   trn_loss:88.1869   tst_loss:95.5334   tst_nll:75.0396   tst_kl:20.4939   sum_norm_grad:435.1315\n",
      "it:30001   ms/it:8.2572   trn_loss:88.9855   tst_loss:95.1945   tst_nll:74.7884   tst_kl:20.4061   sum_norm_grad:532.7263\n",
      "it:30251   ms/it:8.2379   trn_loss:93.3942   tst_loss:95.9549   tst_nll:75.8224   tst_kl:20.1325   sum_norm_grad:537.1184\n",
      "it:30501   ms/it:8.1763   trn_loss:95.9863   tst_loss:95.2355   tst_nll:74.6904   tst_kl:20.5450   sum_norm_grad:443.2344\n",
      "it:30751   ms/it:8.1587   trn_loss:103.2956   tst_loss:95.7448   tst_nll:74.8156   tst_kl:20.9292   sum_norm_grad:639.9230\n",
      "it:31001   ms/it:8.2373   trn_loss:99.6281   tst_loss:96.0330   tst_nll:75.3437   tst_kl:20.6892   sum_norm_grad:509.9691\n",
      "it:31251   ms/it:8.2642   trn_loss:93.2277   tst_loss:96.5316   tst_nll:74.8011   tst_kl:21.7304   sum_norm_grad:565.1442\n",
      "it:31501   ms/it:8.2399   trn_loss:98.8137   tst_loss:94.8659   tst_nll:74.2961   tst_kl:20.5699   sum_norm_grad:487.9633\n",
      "it:31751   ms/it:8.2390   trn_loss:89.9007   tst_loss:95.9717   tst_nll:74.6950   tst_kl:21.2767   sum_norm_grad:323.7951\n",
      "it:32001   ms/it:8.2598   trn_loss:92.0165   tst_loss:95.5847   tst_nll:74.3418   tst_kl:21.2429   sum_norm_grad:544.3785\n",
      "it:32251   ms/it:8.2922   trn_loss:91.8557   tst_loss:95.3442   tst_nll:74.9442   tst_kl:20.4000   sum_norm_grad:354.7590\n",
      "it:32501   ms/it:8.2118   trn_loss:93.8079   tst_loss:94.9228   tst_nll:74.1481   tst_kl:20.7746   sum_norm_grad:496.3012\n",
      "it:32751   ms/it:8.2230   trn_loss:92.0644   tst_loss:96.2702   tst_nll:75.1148   tst_kl:21.1554   sum_norm_grad:502.8069\n",
      "it:33001   ms/it:8.2497   trn_loss:86.3031   tst_loss:94.8656   tst_nll:73.5262   tst_kl:21.3394   sum_norm_grad:398.3834\n",
      "it:33251   ms/it:8.2422   trn_loss:90.9470   tst_loss:95.6094   tst_nll:74.4927   tst_kl:21.1166   sum_norm_grad:518.0490\n",
      "it:33501   ms/it:8.1715   trn_loss:94.1972   tst_loss:95.5603   tst_nll:74.5368   tst_kl:21.0235   sum_norm_grad:491.9893\n",
      "it:33751   ms/it:8.1740   trn_loss:84.3660   tst_loss:96.0006   tst_nll:75.3154   tst_kl:20.6852   sum_norm_grad:399.3826\n",
      "it:34001   ms/it:8.2510   trn_loss:96.6165   tst_loss:95.5739   tst_nll:74.1825   tst_kl:21.3914   sum_norm_grad:598.1465\n",
      "it:34251   ms/it:8.2853   trn_loss:91.1956   tst_loss:95.6995   tst_nll:74.0909   tst_kl:21.6086   sum_norm_grad:722.1900\n",
      "it:34501   ms/it:8.2397   trn_loss:85.3465   tst_loss:94.9647   tst_nll:74.0027   tst_kl:20.9620   sum_norm_grad:372.8212\n",
      "it:34751   ms/it:8.2395   trn_loss:95.9603   tst_loss:95.6924   tst_nll:74.0264   tst_kl:21.6659   sum_norm_grad:512.9751\n",
      "it:35001   ms/it:8.2757   trn_loss:89.3138   tst_loss:94.2024   tst_nll:73.4701   tst_kl:20.7323   sum_norm_grad:539.6708\n",
      "it:35251   ms/it:8.2877   trn_loss:104.4182   tst_loss:95.7220   tst_nll:74.9508   tst_kl:20.7712   sum_norm_grad:591.6014\n",
      "it:35501   ms/it:8.1780   trn_loss:89.0770   tst_loss:94.6851   tst_nll:73.9579   tst_kl:20.7272   sum_norm_grad:493.3982\n",
      "it:35751   ms/it:8.2371   trn_loss:96.2822   tst_loss:95.2431   tst_nll:73.9900   tst_kl:21.2531   sum_norm_grad:616.2849\n",
      "it:36001   ms/it:8.2805   trn_loss:104.2974   tst_loss:95.0059   tst_nll:74.5361   tst_kl:20.4698   sum_norm_grad:598.4661\n",
      "it:36251   ms/it:8.2790   trn_loss:92.3718   tst_loss:95.6937   tst_nll:73.8834   tst_kl:21.8104   sum_norm_grad:540.7161\n",
      "it:36501   ms/it:8.2373   trn_loss:95.7532   tst_loss:94.5186   tst_nll:73.2902   tst_kl:21.2284   sum_norm_grad:544.5507\n",
      "it:36751   ms/it:8.2614   trn_loss:92.3881   tst_loss:95.6637   tst_nll:74.2255   tst_kl:21.4381   sum_norm_grad:556.7919\n",
      "it:37001   ms/it:8.2704   trn_loss:89.5498   tst_loss:94.5648   tst_nll:73.0089   tst_kl:21.5559   sum_norm_grad:669.0724\n",
      "it:37251   ms/it:8.2494   trn_loss:81.2119   tst_loss:94.8074   tst_nll:73.6568   tst_kl:21.1506   sum_norm_grad:470.7941\n",
      "it:37501   ms/it:8.2374   trn_loss:91.9064   tst_loss:94.9572   tst_nll:74.0324   tst_kl:20.9249   sum_norm_grad:526.6972\n",
      "it:37751   ms/it:8.2555   trn_loss:95.1651   tst_loss:95.0565   tst_nll:74.1256   tst_kl:20.9309   sum_norm_grad:482.9742\n",
      "it:38001   ms/it:8.2687   trn_loss:94.9950   tst_loss:95.4203   tst_nll:74.6256   tst_kl:20.7947   sum_norm_grad:685.8509\n",
      "it:38251   ms/it:8.2352   trn_loss:87.7089   tst_loss:95.3314   tst_nll:74.1835   tst_kl:21.1479   sum_norm_grad:484.6642\n",
      "it:38501   ms/it:8.2450   trn_loss:96.3948   tst_loss:95.3057   tst_nll:74.1131   tst_kl:21.1926   sum_norm_grad:477.4860\n",
      "it:38751   ms/it:8.2741   trn_loss:91.0143   tst_loss:96.1284   tst_nll:74.4671   tst_kl:21.6613   sum_norm_grad:516.8703\n",
      "it:39001   ms/it:8.2332   trn_loss:93.1803   tst_loss:94.5465   tst_nll:73.6825   tst_kl:20.8640   sum_norm_grad:546.8208\n",
      "it:39251   ms/it:8.2147   trn_loss:94.1186   tst_loss:95.2316   tst_nll:74.7130   tst_kl:20.5187   sum_norm_grad:585.1824\n",
      "it:39501   ms/it:8.2274   trn_loss:85.8579   tst_loss:95.2314   tst_nll:73.7965   tst_kl:21.4348   sum_norm_grad:454.3126\n",
      "it:39751   ms/it:8.2873   trn_loss:89.4100   tst_loss:95.4110   tst_nll:74.6880   tst_kl:20.7229   sum_norm_grad:574.0444\n",
      "it:40001   ms/it:8.2554   trn_loss:93.0305   tst_loss:94.0303   tst_nll:73.2089   tst_kl:20.8214   sum_norm_grad:370.2800\n",
      "it:40251   ms/it:8.2352   trn_loss:94.4651   tst_loss:95.8122   tst_nll:73.9440   tst_kl:21.8682   sum_norm_grad:518.2649\n",
      "it:40501   ms/it:8.2360   trn_loss:93.1322   tst_loss:94.2561   tst_nll:73.1101   tst_kl:21.1460   sum_norm_grad:443.4222\n",
      "it:40751   ms/it:8.2455   trn_loss:94.1579   tst_loss:95.1274   tst_nll:73.9682   tst_kl:21.1592   sum_norm_grad:590.7770\n",
      "it:41001   ms/it:8.2458   trn_loss:94.5556   tst_loss:93.4816   tst_nll:72.9166   tst_kl:20.5649   sum_norm_grad:401.8537\n",
      "it:41251   ms/it:8.2261   trn_loss:82.3316   tst_loss:95.4182   tst_nll:74.5317   tst_kl:20.8865   sum_norm_grad:666.6778\n",
      "it:41501   ms/it:8.2904   trn_loss:107.5355   tst_loss:94.3706   tst_nll:73.0945   tst_kl:21.2761   sum_norm_grad:633.9945\n",
      "it:41751   ms/it:8.2533   trn_loss:102.3969   tst_loss:94.1628   tst_nll:73.5858   tst_kl:20.5769   sum_norm_grad:727.9357\n",
      "it:42001   ms/it:8.2422   trn_loss:87.7422   tst_loss:94.1707   tst_nll:73.1421   tst_kl:21.0286   sum_norm_grad:473.5380\n",
      "it:42251   ms/it:8.2345   trn_loss:90.3090   tst_loss:94.8594   tst_nll:74.3117   tst_kl:20.5477   sum_norm_grad:480.7428\n",
      "it:42501   ms/it:8.2752   trn_loss:90.7338   tst_loss:94.3450   tst_nll:73.5954   tst_kl:20.7496   sum_norm_grad:552.8487\n",
      "it:42751   ms/it:8.2624   trn_loss:97.9351   tst_loss:94.3638   tst_nll:73.5087   tst_kl:20.8551   sum_norm_grad:566.5553\n",
      "it:43001   ms/it:8.1799   trn_loss:93.4709   tst_loss:94.7935   tst_nll:73.6575   tst_kl:21.1360   sum_norm_grad:589.3351\n",
      "it:43251   ms/it:8.2390   trn_loss:93.8279   tst_loss:94.8600   tst_nll:73.7775   tst_kl:21.0824   sum_norm_grad:819.6432\n",
      "it:43501   ms/it:8.2791   trn_loss:95.1309   tst_loss:94.9538   tst_nll:73.8149   tst_kl:21.1389   sum_norm_grad:641.3374\n",
      "it:43751   ms/it:8.2810   trn_loss:88.6112   tst_loss:94.5549   tst_nll:73.6116   tst_kl:20.9433   sum_norm_grad:782.4581\n",
      "it:44001   ms/it:8.2794   trn_loss:92.6073   tst_loss:93.8861   tst_nll:72.9349   tst_kl:20.9513   sum_norm_grad:444.0027\n",
      "it:44251   ms/it:8.3472   trn_loss:90.3468   tst_loss:94.8443   tst_nll:73.8619   tst_kl:20.9823   sum_norm_grad:496.5469\n",
      "it:44501   ms/it:8.2447   trn_loss:94.1757   tst_loss:94.2362   tst_nll:73.9904   tst_kl:20.2458   sum_norm_grad:657.1694\n",
      "it:44751   ms/it:8.2415   trn_loss:91.1105   tst_loss:94.8063   tst_nll:73.1909   tst_kl:21.6155   sum_norm_grad:372.2267\n",
      "it:45001   ms/it:8.2673   trn_loss:91.7606   tst_loss:94.0004   tst_nll:73.1480   tst_kl:20.8524   sum_norm_grad:719.2126\n",
      "it:45251   ms/it:8.2901   trn_loss:97.6344   tst_loss:94.6105   tst_nll:73.5537   tst_kl:21.0568   sum_norm_grad:524.6968\n",
      "it:45501   ms/it:8.2223   trn_loss:96.7768   tst_loss:94.1077   tst_nll:73.0954   tst_kl:21.0123   sum_norm_grad:557.7588\n",
      "it:45751   ms/it:8.2532   trn_loss:88.5243   tst_loss:94.5430   tst_nll:73.4593   tst_kl:21.0837   sum_norm_grad:549.5432\n",
      "it:46001   ms/it:8.2846   trn_loss:95.0143   tst_loss:94.1733   tst_nll:72.7262   tst_kl:21.4471   sum_norm_grad:721.0759\n",
      "it:46251   ms/it:8.2655   trn_loss:92.8926   tst_loss:95.6013   tst_nll:73.6601   tst_kl:21.9412   sum_norm_grad:847.6617\n",
      "it:46501   ms/it:8.2790   trn_loss:89.3002   tst_loss:94.7222   tst_nll:72.9084   tst_kl:21.8138   sum_norm_grad:647.9052\n",
      "it:46751   ms/it:8.3193   trn_loss:89.6552   tst_loss:94.6328   tst_nll:73.5012   tst_kl:21.1316   sum_norm_grad:453.8050\n",
      "it:47001   ms/it:8.2748   trn_loss:91.9704   tst_loss:94.1757   tst_nll:73.4060   tst_kl:20.7697   sum_norm_grad:817.0945\n",
      "it:47251   ms/it:8.2459   trn_loss:93.0032   tst_loss:93.8077   tst_nll:72.8963   tst_kl:20.9114   sum_norm_grad:604.6274\n",
      "it:47501   ms/it:8.2840   trn_loss:93.3490   tst_loss:94.9580   tst_nll:73.0902   tst_kl:21.8678   sum_norm_grad:429.7482\n",
      "it:47751   ms/it:8.2879   trn_loss:87.7900   tst_loss:94.3695   tst_nll:72.8856   tst_kl:21.4839   sum_norm_grad:539.5405\n",
      "it:48001   ms/it:8.2563   trn_loss:98.2043   tst_loss:93.3153   tst_nll:72.1551   tst_kl:21.1602   sum_norm_grad:623.7249\n",
      "it:48251   ms/it:8.2457   trn_loss:100.6152   tst_loss:94.2872   tst_nll:73.7673   tst_kl:20.5199   sum_norm_grad:677.5202\n",
      "it:48501   ms/it:8.2771   trn_loss:88.7600   tst_loss:93.7643   tst_nll:72.6830   tst_kl:21.0813   sum_norm_grad:454.2632\n",
      "it:48751   ms/it:8.3455   trn_loss:96.5667   tst_loss:94.6928   tst_nll:73.5563   tst_kl:21.1365   sum_norm_grad:605.6883\n",
      "it:49001   ms/it:8.2370   trn_loss:97.5158   tst_loss:94.2065   tst_nll:73.1295   tst_kl:21.0770   sum_norm_grad:442.5939\n",
      "it:49251   ms/it:8.2352   trn_loss:96.8186   tst_loss:94.0567   tst_nll:72.9796   tst_kl:21.0771   sum_norm_grad:573.3347\n",
      "it:49501   ms/it:8.2618   trn_loss:95.7419   tst_loss:94.3354   tst_nll:73.4407   tst_kl:20.8948   sum_norm_grad:905.2293\n",
      "it:49751   ms/it:8.2658   trn_loss:93.3351   tst_loss:95.1076   tst_nll:73.0878   tst_kl:22.0198   sum_norm_grad:422.7823\n",
      "it:50000   ms/it:8.2503   trn_loss:96.9131   tst_loss:93.8293   tst_nll:72.3012   tst_kl:21.5281   sum_norm_grad:2663.0032\n"
     ]
    }
   ],
   "source": [
    "num_train_epochs = 1.  # @param { isTemplate: true}\n",
    "num_evals = 200        # @param { isTemplate: true}\n",
    "\n",
    "dur_sec = dur_num = 0\n",
    "num_train_steps = int(num_train_epochs * train_size)\n",
    "for i in range(num_train_steps):\n",
    "  start = time.time()\n",
    "  trn_loss, (trn_nll, trn_kl), g = fit()\n",
    "  stop = time.time()\n",
    "  dur_sec += stop - start\n",
    "  dur_num += 1\n",
    "  if i % int(num_train_steps / num_evals) == 0 or i == num_train_steps - 1:\n",
    "    tst_loss, (tst_nll, tst_kl) = eval()\n",
    "    f, x = zip(*[\n",
    "        ('it:{:5}', opt.iterations),\n",
    "        ('ms/it:{:6.4f}', dur_sec / max(1., dur_num) * 1000.),\n",
    "        ('trn_loss:{:6.4f}', trn_loss),\n",
    "        ('tst_loss:{:6.4f}', tst_loss),\n",
    "        ('tst_nll:{:6.4f}', tst_nll),\n",
    "        ('tst_kl:{:6.4f}', tst_kl),\n",
    "        ('sum_norm_grad:{:6.4f}', sum(g)),\n",
    "\n",
    "    ])\n",
    "    print('   '.join(f).format(*[getattr(x_, 'numpy', lambda: x_)()\n",
    "                                 for x_ in x]))\n",
    "    sys.stdout.flush()\n",
    "    dur_sec = dur_num = 0\n",
    "  # if i % 1000 == 0 or i == maxiter - 1:\n",
    "  #   encoder.save('/tmp/encoder.npz')\n",
    "  #   decoder.save('/tmp/decoder.npz')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "G1ImqkK7xAv1"
   },
   "source": [
    "### 6  Evaluate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "H2y4Dj3G6UI9"
   },
   "outputs": [],
   "source": [
    "# We'll just examine ten random digits.\n",
    "x = next(iter(eval_dataset.batch(100)))\n",
    "xhat = decoder(encoder(x).sample())\n",
    "assert isinstance(xhat, tfd.Distribution)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "height": 524
    },
    "colab_type": "code",
    "id": "u7Gdw1Ce62UF",
    "outputId": "c1216e5d-7ff3-400e-c3f1-8ea4ef5c0876"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Originals:\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 10000x200 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Decoded Random Samples:\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 10000x200 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Decoded Modes:\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 10000x200 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Decoded Means:\n"
     ]
    },
    {
     "data": {
      "image/png": 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KcWqzw3nH8y/TTz89ADvv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\nPfXUGGte++23X9DkT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MUx5Me1erx8TshHctv/8ccfj/ZNN90EwAwzzBCy5ZZbDij7oaef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\niv3d15Pv32effTZQ3t+7a+0NP/zw0Z588smBsu5wP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QBcdNFFIXMd1HR8r/r4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AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAMFIWGAQAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA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\nYII=\n",
      "text/plain": [
       "<Figure size 10000x200 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "print('Originals:')\n",
    "tfn.util.display_imgs(x);\n",
    "\n",
    "print('Decoded Random Samples:')\n",
    "tfn.util.display_imgs(xhat.sample());\n",
    "\n",
    "print('Decoded Modes:')\n",
    "tfn.util.display_imgs(xhat.mode());\n",
    "\n",
    "print('Decoded Means:')\n",
    "tfn.util.display_imgs(xhat.mean());"
   ]
  }
 ],
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